Rewrite as a simplified fraction. ${2.\overline{69} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 269.6969...\\ 1x &= 2.6969...\end{align*}}$ Subtracting the two equations, we have: ${99x = 267}$ ${x = \dfrac{267}{99}} $ ${x = \dfrac{89}{33}} \text{or} {2 \dfrac{23}{33}}$